For example, an engine mounted in a motorcycle is configured in such a manner that a crankshaft and a camshaft are rotatable in association with each other via a rotation transmission mechanism such as a chain and sprockets, and an intake valve and an exhaust valve are driven to be opened and closed at specified timings by a cam mounted to the camshaft. To be specific, the cam has a unique profile, and causes each valve to be opened and closed by predetermined opening and closing degrees at specified opening and closing timings, according to the profile. When the intake valve is opened, an air-fuel mixture is suctioned into a combustion chamber of the engine. The air-fuel mixture is compressed by a piston, and is thereafter ignited at a specified timing to be combusted. The resulting combustion gas is expanded to push the piston back, causing the crankshaft to rotate. When the exhaust valve is opened, the combustion gas is exhausted from the combustion chamber.
Desired opening and closing timings of the valves vary according to an engine speed of the engine. For example, during an idling state, it is desirable to lessen a time period (overlap time) when the intake valve and the exhaust valve are both opened in order to stabilize combustion, while during a high-speed rotation state, it is desirable to retard a timing when the intake valve is closed to increase charging efficiency of intake air to gain a high output power.
As should be appreciated from the above, it is necessary to open and close the valves at timings according to the engine speed of the engine in order to suitably run the engine. As a conventional engine mounted in four-wheel automobiles to achieve the above purpose, an engine equipped with a hydraulic variable valve timing system is disclosed in, for example, Japanese Laid-Open Patent Application Publication Nos. Hei. 11-132016, 11-280430, 11-324629 and 2002-242616. The hydraulic variable valve timing system disclosed here includes a cam pulley which has an inner space and is rotatable in association with a crankshaft and a rotor which is accommodated in the inner space and mounted to an end portion of the camshaft. The inner space of the cam pulley is partitioned into an advanced angle space and a retarded angle space by the rotor. To which of these spaces a hydraulic oil is to be fed is controlled by an oil control valve operable in response to a command from a controller. By a pressure of the hydraulic oil fed, a rotational phase of the rotor with respect to the cam pulley is changed, thus controlling the opening and closing timings of the valves.
The controller is typically configured to calculate an operation amount of the oil control valve by proportional-integral control (PI control) using the engine speed and to output a command signal to drive the oil control valve based on a calculation result. The configuration is disclosed in, for example, Japanese Laid-Open Patent Application Publication No. Hei. 11-2140. Also, Japanese Patent Publication No. 3616734 discloses a so-called sliding mode control intended for the hydraulic control system.
However, in the hydraulic variable valve timing system subjected to the PI control, overshooting is likely to occur. In contrast, in a hydraulic variable valve timing system subjected to proportional control, due to a viscosity change of the hydraulic oil which may occur with a temperature change, mechanical manufacturing errors of the variable valve timing system or the oil control valve, etc., a deviation will result from the event that a position of the rotor has converged before reaching a target value. Therefore, it is desirable to control a gain based on temperature of the hydraulic oil to execute general proportional control, integral control, differential control, and a combination of these. But, it is not easy to control the gain correctly.